Tyrone Rees


Tyrone Rees is a researcher in the numerical analysis group at the STFC Rutherford Appleton Laboratory. He completed his DPhil with Andy Wathen at the University of Oxford on Preconditioning iterative methods for PDE constrained optimization. Prior to joining RAL he spent two years as a postdoctoral fellow at the University of British Columbia in Vancouver, Canada.

His research interests lie in the field of numerical linear algebra. He is particularly interested in the use of iterative methods to solve large, sparse systems of equations, and the acceleration of such methods using precondtioners. As well as theoretical issues surrounding these methods he is also interested using them to efficiently solve problems from applications, with a particular interest in the systems arising in the optimal control of PDEs.

  • Krylov subspace methods
  • Preconditioning
  • PDE constrained optimization
  1. Rees, T., The iterative solution of linear systems arising in the primal-dual interior point algorithm for linear programming RAL Preprint RAL-P-2016-007, (Submitted) 2016 link BibTeX
  2. Rees, T. and Scott, J., The null-space method and its relationship with matrix factorizations for sparse saddle point systems, RAL Technical Report RAL-TR-2014-016, (Submitted) 2014 link BibTeX
  3. Pestana, J. and Rees, T., Null-space preconditioners for saddle point systems RAL Technical Report RAL-TR-2015-003, 2015 (to appear, SIMAX) link BibTeX
  4. Greif, C., Rees, T. and Szyld, D. B., Multi-preconditioned GMRES, UBC CS TR-2011-12, 2016 (to appear, SeMA). link code BibTeX
  5. Barker, A. T., Rees, T. and Stoll, M., A fast solver for an H1 regularized optimal control problem, Communications in Computational Physics, 19(01), 143-167, 2016. link BibTeX
  6. Gould, N.I.M., Orban, D. and Rees, T., Projected Krylov methods for saddle-point systems, SIAM. J. Matrix Anal. & Appl., 35(4), 1329–1343, 2014. link BibTeX
  7. Greif, C., Rees, T. and Szyld, D. B., Additive Schwarz with Variable Weights, Domain Decomposition Methods in Science and Engineering XXI, 2014 link BibTeX
  8. Rees, T. and Wathen, A.J., Preconditioning iterative methods for the optimal control of the Stokes equations, SIAM J. Sci. Comput., Vol. 33, pp. 2903-2926, 2011. link BibTeX
  9. Rees, T., Stoll, M. and Wathen, A.J., All-at-once preconditioning in PDE-constrained optimization. Kybernetika, Vol 45., pp. 341-360, 2010 link BibTeX
  10. Rees, T. and Stoll, M., Block triangular preconditioners for PDE-constrained optimization. Numerical Linear Algebra with Applications, Vol. 17, pp. 977-996, 2010. link BibTeX
  11. Rees, T., Dollar, H.S. and Wathen, A. J., Optimal solvers for PDE-Constrained Optimization, SIAM J. Sci. Comput., Vol. 32, pp. 271-298, 2010. link code BibTeX
  12. Wathen, A. J. and Rees, T., Chebyshev semi-iteration in preconditioning for problems including the mass matrix, Electronic Transactions on Numerical Analysis, Volume 34 pp. 125-135, 2009 link BibTeX

DPhil Thesis

  • Preconditioning Iterative Methods for PDE Constrained Optimization link


  • SIAM Conference on Applied Linear Algebra, Atlanta, 25-30/10/2015. Co-organizer and speaker in minisymposium "Linear Algebra for PDE-constrained Optimization"

Past events

  • Strathclyde Biennial conference on Numerical Analysis, Glasgow, 23-26/06/2015. Spoke in minisymposium "Numerical linear algebra for optimisation and data assimilation"
  • Preconditioning 2015, Eindhoven, 17-19/06/2015. Photo
  • 4th IMA Conference on Numerical Linear Algebra and Optimisation, Birmingham, 3-5/09/2014. Spoke in minisymposium "Preconditioning for PDEs and Optimization"
  • Householder Symposium, Spa, Belgium, 8-13/06/2014. Presented poster "Preconditioning Linear Systems arising in Constrained Optimization Problems" (awarded best poster prize).
  • International Conference on Applied Mathematical Optimization and Modelling (APMOD) 2014, Warwick, 9-11/04/2014. Spoke in minisymposium "Linear Algebra for Large-Scale Optimization Problems"
  • Strathclyde Biennial conference on Numerical Analysis, Glasgow, 24-28/06/2013. Spoke in minisymposium "Developments in Preconditioners and Iterative Methods for Linear Systems"
  • Preconditioning 2013, Oxford, 19-21/06/2013. Photo
  • 3rd IMA Conference on Linear Algebra and Optimization, Birmingham, 10-12/09/2012. Presented talk "A multi-preconditioned GMRES algorithm"
  • SIAM Conference on Applied Linear Algebra, Valencia, Spain 18-22/07/2012. Spoke in Minisymposium "Recent advances in fast iterative solvers" Photo Photo
  • ICIAM, Vancouver, British Columbia 18-22/07/2011. Spoke in Minisymposia "New developments in iterative solvers for large sparse problems" and "Multigrid Methods for the Indefinite Helmholtz Equation"
  • Householder Symposium, Tahoe City, California, 13-17/06/2011. Presented "A multiprecondioned GMRES algorithm".
  • SIAM confererence on Optimization, Darmstadt, Germany, 16-19/05/2011. Presented "Multipreconditioned GMRES with applications in PDE constrained optimization" in minisymposium "Preconditioning linear systems in large-scale optimization".
  • GAMM Annual Meeting, Karlsruhe, Germany, 22-26/03/2010. Spoke in Young Researchers Minisymosium "Numerical Linear Algebra and Optimization".
  • SIAM Annual Meeting, Denver, Colorado, USA, 6-10/07/2009. Spoke in minisymposium "Solvers for PDE constrained optimization". Awarded SIAM Student Travel Award to attend the meeting.
  • 23rd Biennial Conference on Numerical Analysis, Glasgow, UK, 23-26/07/2009. Spoke in minisymopsium "PDE constrained optimization". Talk was "highly commended" in the student presentation competition.
  • Advances and Perspectives on Numerical Methods for Saddle Point Problems, Banff, Alberta, Canada, 12-17/04/2009 (Invited). Photo
  • 1st Elgersburg School on Mathematical Systems Theory, Elgersburg, Germany, 30/03/2009 - 3/04/2009. Awarded full scholarship to attend. Photo
  • LMS Symposium on Computational Linear Algebra for Partial Differential Equations, Durham, UK, 14-24/07/2008(Invited). Photo
  • 10th Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado, USA, 6-11/04/2008. Awarded accommodation and conference fees for the student paper competition..
  • IMA International Conference on Numerical Linear Algebra and Optimisation, Birmingham, UK, 13-15/09/2007.
  • 22nd Biennial Conference on Numerical Analysis, Dundee, UK, 26-29/06/2007.
Principal author Contributing author See also my GitHub profile.